Aaron Rodgers 37 times!
John Elway was sacked 516 times during his career. He is followed by Dave Krieg with 494
As of the 2007 season, the quarterback who was sacked the most times in a season was David Carr of the Houston Texans who was sacked 76 times in 2002.
In the NFL through the 2008 season, that is David Carr of the 2002 Houston Texans who was sacked 76 times.
That would be John Elway, sacked 516 times in his career.
Matt Cassel, sacked 47 times in 2008.